First, it is worth noting that much of what we call "positive economics" is based on weak ethical considerations, namely Pareto improvements.
But, Pareto gets in the way whenever a policy would harm one group (or individual) in order to benefit others (that is, most policies). We cannot compare utility across people--we have no basis for saying, for example, that imposing a small dis-utility on one individual while improving the utility of thousands of others is an improvement. (There is the notion of "Kaldor-Hicks efficiency" (aka potential Pareto improvements), but that is controversial in itself.)
The utilitarians (J.S. Mill, Behtham) posited that economics should seek to maximize overall utility of a group or society. I'll leave the philosophical debate to the welfare economists, but in practice we cannot know what the social welfare function (SWF) of a society is. Thus, even if our philosophy dictated that we switch to a utilitarian economics, it is difficult to see how we would go about it. (That said, we use the concept of Benthamite utility functions quite often in theoretical work.) This leaves us, again, with Pareto's criterion for applied work.
But, economics does have much to say about normative questions. Many applied economists draw a sharp distinction between policy and economics. Namely, while in many cases, we cannot propose a particular goal (e.g. increasing health funding), we can analyze the impacts of such policies. Using the healthcare spending example, an economist would be unable to answer the question of "should we increase healthcare spending." We can, however, give some insights into the impacts of various mechanisms for increasing spending, and perhaps even rank various ways of achieving a goal.
Economics is not alone in this regard. An engineer, for example, can propose ways of reducing energy usage, but which technology bundle is ultimately adopted is a matter of economics and policy. Similarly, economists can comment on the various impacts (potential inefficiencies, distortions...) of policies, but in many cases cannot say which one to adopt.
A classic example is the free trade debate. Almost all economic models show an overall gain from trade (and, indeed, usually potential Pareto improvements, depending on the policy), but the same models also tell us that some are harmed by many trade policies (be it liberalization or restriction). Asked whether trade liberalization is a good thing, many economists would answer "for whom?" and "it depends." Asked whether trade policy X is good for consumers in country Y, a more concrete answer would be offered.
So, normative questions can most certainly be answered if the policy goals (ethical criteria) are stated explicitly. This sharp distinction between economics and policy seems to be less-clear to non-economists, and that leads to many misunderstandings of what economists do, and what sorts of questions economics can answer.